Israeli Prime Minister Benjamin Netanyahu said Sunday that Israel is not obliged to continue to abide by cease-fire requests in the Gaza war as long as Hamas continues to fire rockets during those periods.

Fighting resumes in Gaza as cease-fire crumbles

In an interview on CBS' "Face the Nation" Sunday, Netanyahu said Israel had accepted and implemented five cease-fires that Hamas had rejected, adding the Gaza Strip rulers were even continuing to fire rockets during a 24-hour truce they themselves proposed.

"Israel is not obliged and will not let a terrorist organization, a ruthless terror organization, committed to our destruction, to decide when it's convenient for them to stop for a moment, rearm, and continue firing on our citizens and our people," Netanyahu said. "We'll determine what is important for our own security in the way that we can to protect our people, including working against these terror tunnels that they're digging against us. That's how we'll act. We'll just act to protect our people."

He declined to say whether there would be an expansion of the Israeli ground offensive inside of Gaza that is aimed at destroying tunnels built by the militant group to carry out attacks on Israel.

Netanyahu said the offensive has uncovered "this vast underground terror kingdom, these vast tunnels in which they pulled in tens of thousands of tons of concrete." He said the concrete used in the tunnels was meant to help rebuild the city, but was appropriated for the tunnels "that are meant to come in under our communities and blow up our kids and kidnap our people."

"That's why I think that the economic and social relief that people want to have for Gaza, and that we want to have for the people of Gaza once this is over with, is tied to demilitarization," Netanyahu argued. "We'd have to, as this example shows, make sure the concrete that is brought in is not abused and brought to dig in new tunnels. We'd have to make sure that money that people want to go for the people of Gaza, for their social relief, and we have no objection to that, is not used for buying rockets and missiles and drones and everything else that Hamas is using against us."

He said discrediting and demilitarizing Hamas might allow a more moderate force to come to power representing the Palestinians - one with which the Israelis feel they can negotiate "to get a better future for all of us."

The details of demilitarization would have to be discussed once all sides agree to an "unconditional effort to try to address these problems" being sought by the Egyptians, he said.

"How do we prevent stuff from coming in? What are we targeting vis-à-vis social and economic relief? How do we make sure that money or materials that go in are not used for re-militarizing Gaza? There are ways of doing this. I think it's important to put that out as an overriding goal, and it will have to be discussed in Egypt when the time comes," he said.

Madeleine Albright: "To put it mildly, the world is a mess"

But Former Secretary of State Madeleine Albright said that getting to these discussions will be a very difficult task.

"The United States can put down all kinds of plans, but until there's political will between the parties themselves, it's very hard to have anything happen," she said in a separate interview on "Face the Nation." She praised the current Secretary of State, John Kerry, for doing everything he can to prolong the short cease-fires and try to get both sides to a negotiating table, but noted that there are still questions about "what are the preconditions for even getting to discussing the conditions?"

"Hamas is responsible for these civilian deaths. Hamas is not only trying to kill our people, it's sacrificing its own people, quite willfully, deliberately, cynically and horribly. They are using their people as human shields," he said. "They want the bodies of the Palestinian civilians to pile up. And every time we see a dead civilian, you know, we regret it deeply."

Albright said she agreed with Israel's efforts at self-defense but was worried about what the world thinks about the ongoing conflict.

"I am concerned about Israel. I am a great believer in the security of Israel and the moral authority of the Israelis. But I am very worried about what is going on in terms of their image," she said.